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The Practice of Statistics - Chapter 2
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Terms in this set (23)
Percentile
of the a distribution is the value with p percent of the observations less than it.
ex - jenny made an 86 and she is 4th from the top of the class, so out of 25 students, 21 are below her. 21/25 = 84.. so jenny is at the 84th percentile.
relative frequency
divide the count in each class by the total number there were. Multiply by 100 to convert it to percent.
Cumulative frequency
add the counts in the frequency column for the current class and all classes with smaller values of the variable.
Cumulative relative frequency
divide cumulative frequency by total number overall and then multiply by 100 to get percent.
Cumulative relative frequency graph
A plot of the cummulative relative frequency in each class at the smallest value of the next class
A CRF graph can be used to describe the position of an individual within a distribution or locate a specific percentile of the distribution
Standardized value
if x is an observation from the distribution that has known men and SD, the z-score is..
- tells us how many SD the from the mean an observed value falls, and in what direction.
Effect of adding (or subtracting) a constant
Adding the same number A (either positive, zero, or negative) to each observation
- adding A to a measures of centers and location (mean, median, quartiles, percentiles), but
- doesn't change the shape of the distribution or measures of spread (range, IQR, SD)
Effect of multiplying (or dividing) by a constant
Multiplies (or divides) measures of center, location (mean, median, quartiles, percentiles), and spread (range, IQR, SD). Does not change the shape of the distribution.
Density Curve
- is always on or above the horizontal axis
- has area exactly 1 underneath it
A ___ describes the overall pattern of the distribution. The area under the curve and above any interval of values on the horizontal axis is the proportion of all observations that fall in that interval.
Median of a density curve
is the equal-areas point, the point that divides the area under the curve in half
Mean of a density curve
is the balance point, at which the curve would balance if made of solid material.
Normal curves
- have same overall shape: symmetric, single-peaked, and bell-shaped.
- completely described by mean and SD
Normal Distribution
is described by a Normal density curve. Any particular Normal distribution is completely specified by two numbers: its mean and SD.
we abbreviate normal distribution with mean μ and SD σ as N(μ, σ).
Normal Curve
The mean of a normal distribution is at the center of the symmetric _____.
68-95-99.7 rule
In the Normal distribution with
mean μ and standard deviation σ,
- Approx. 68% of the observations fall within σ of the mean μ
-Approx. 95% of the observations fall within 2σ of the mean μ
- Approx. 99.7% of the observations fall within 3σ of the mean μ
Chebyshev's Inequality
applies to all distributions and not just normal distributions like the 68-95-99.7 rule.
1-(1/k^2) k=SD
Standard Normal Distribution
A normal distribution with a mean of 0 and a standard deviation of 1.
The Standard Normal Table
Table A is a table of areas under the standard normal curve. The table entry for each value z is the area under the curve to the left of z.
Normal distribution function
A function defined by 2 variables: μ ( mu, the population mean) and σ (sigma, the population standard deviation).
= N(μ, σ)
noramalcdf
to find areas under a normal curve
invnorm
calculates the value corresponding to a given percentile in a Normal distribution
Normality
Being within certain limits that define the range of normal distribution functioning. Normality of a distribution can be assessed using a Normal Probability Plot.
Normal Probability Plot
a display to help assess whether a distribution of data is approximately normal. It plots the observed data versus theoretical data generated using normal function. If the plot is nearly straight, the data satisfy the nearly normal condition
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